For each weak \(T\) -linkage computed from the previous stage, they apply the algorithm by Schrijver [1]}.
Given a weak \(T\) -linkage \(\mathcal {W}\)  of \(G\) , Schrijver [1]} presented an \(O(n^6)\) -time algorithm
for computing a \(T\) -linkage \(\mathcal {P}\)  of \(G\)  such that \(\psi _{\mathcal {W}}\)  is homologous to \(\psi _{\mathcal {P}}\) ,
where \(\phi _{\mathcal {W}}\)  and \(\phi _{\mathcal {P}}\)  are flow functions representing \(\mathcal {W}\)  and \(\mathcal {P}\) , respectively.
Due to Lemma REF , this algorithm always returns a \(T\) -linkage \(\mathcal {P}^{\prime }\)  of \(G\) 
if there is a \(T\) -linkage \(\mathcal {P}\)  discretely homotopic to a given weak \(T\) -linkage \(\mathcal {W}\) .
